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When two sound waves travel in the same direction in a medium, the displacements of a particle located at 'x' at time 't' is given by : y1 = 0.05 cos(0.50πx - 100πt) y2 = 0.05 cos(0.46πx - 92πt) where y1, y2 and x are in meters and t in seconds. The speed of sound in the medium is :

1. 92 m/s
2. 200 m/s
3. 100 m/s
4. 332 m/s

Correct answer: 200 m/s

Solution

The speed of sound can be calculated using the wave equation, which relates the angular frequency and wave number. For the first wave, the angular frequency is 100π rad/s and the wave number is 0.50π rad/m, leading to a speed of 200 m/s when calculated using the formula v = ω/k.

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